[4] Barr is best known for representing the International Business Machines Corporation in a 13-year antitrust battle with the federal government, as well as satellite cases by competitors and the EEC.

Other major cases included Powell v. McCormack, over the attempt to exclude Adam Clayton Powell Jr. from taking his seat in the US House of Representatives; the defense of Time Magazine in the libel case brought by Ariel Sharon, relating to the Sabra and Shatila massacre; the effort to recover on behalf of holders of defaulted municipal bonds issued by Washington Public Power Supply System (WPPSS); and the prosecution on behalf of the Federal Deposit Insurance Corporation (FDIC) against Drexel Burnham Lambert and Michael Milken over fraudulent junk bonds.

His major pro bono work included cases for the Lawyers' Committee for Civil Rights Under Law.

Library of Congress Catalog Card Number: 74-603981 In August 1992, Barr along with his partners at Cravath, Swaine & Moore, David Boise and Evan R. Chesler participated in a mock trial of Lee Harvey Oswald at the annual meeting of The American Bar Association.

The Seminar, based at Schloss Leopldskron in Salzburg, Austria "was established in 1947 as a means of bringing together young intellectuals from nations recently at war to discuss topics of mutual interest."

In 1993, Barr was faculty in a seminar called American Law and Legal Institutions, in which United States Supreme Court Justice Stephen Breyer, Lord Slynn of Hadley, and Lloyd N. Cutler also participated.